There aren't any 'likes' (in the Facebook or AO3 kudos sense); you actually have to say if you like something, as in "Oh, I like this" :-D

Memories are bookmarks, basically. It's a way of storing and labelling specific posts that you think are useful and want to refer back to in future (see mine). They're publically visible by default, but they don't have to be -- you can set them to be visible to the owner only. They're certainly not a way of communicating approval, since no-one is notified when you bookmark a new memory...